JEE Main 2026 — 23 January, Evening Shift — Question 22

$\frac{2 \lambda-a+a}{2}=-5 \mu-2 b$ and

$\frac{\mathrm{a}+4 \lambda-\mathrm{a}}{2}=2 \mu+2 \mathrm{~b}$ and

$\frac{2 \lambda-2 \mathrm{a}-2+2}{2}=\mu+\mathrm{a}$

$$\begin{aligned} \Rightarrow & \lambda-\mu=\mathrm{b} \end{aligned}$$

$\lambda-\mu=2 \mathrm{a}$

$\lambda+5 \mu=-2 \mathrm{~b}$

$\Rightarrow\mathrm{~b}=2 \mathrm{a}$

and

$\lambda=\mathrm{a}, \mu=-\mathrm{a}$

$$\begin{aligned} & (a \hat{i}-2 \hat{j}+0 \hat{k}) \cdot(2 \hat{i}+\hat{j}+\hat{k})=0, & 2 a-2=0 & \end{aligned}$$

$a=1 , b=2 a=2 \times 1=2$

$a+b=1+2=3$